<p>This study presents two new numerical methods based on the Bernstein collocation (BC) and Chebyshev collocation (CC) for the solution of coupled generalized homogeneous differential Sylvester matrix equations (CGDSE). By using the derivative operational matrices of Bernstein and Chebyshev polynomials, we convert the matrix equations into a set of linear algebraic equations. We propose an iterative algorithm to efficiently solve the resulting system. We state a rigorous error analysis and derive error equations for the estimation and improvement of the approximate solution. Several numerical experiments are made to show the accuracies and efficiency of the proposed algorithms, which show their utility to solving complicated differential matrix systems.</p>